The ages of a group of 50 women are approximately normally distributedwith a mea

Question

The ages of a group of 50 women are approximately normally distributedwith a mean of 51 years and a standard deviation of 6 years. One woman is randomly selected from the group, and her age is observed. a. Find the probability that her age will fall between 56 and 61 years. b. Find the probability that her age will fall between 49 and 53 years. c. Find the probability that her age will be less than 35 years. d. Find the probability that her age will exceed 41 years E click here to view a table of areas under the standardized normal curve, a. The probability that her age will fall between 56 and 61 years is (Round to three decimal places as needed.)

Explanation / Answer

since a single woman has been drawn , the sample size will not matter.

let X = the age of the selected women.

X~N(51,62)

a. Now, P (56<X<61)

= P(X<61) -P(X<56)

= P(Z<10/6)- P(Z< 5/6) where Z=(X-51)/6 therefore Z~N(0,1)

= 0.95221-0.79767=0.15454

b.P (49<X<53)= 0.63056-0.36944=0.26112
c. P(X<35)=0.00383
d.P(X>41)=1-0.04779=

0.95221

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